Please solve with explanation
1 answer:
Answer:
large area: small area = 100:25 = 4:1
Step-by-step explanation:
Mid-Segment of a triangle is always <u>parallel to the third side</u>, and the length of the midsegment is <u>half the length of the third side</u>.
(x₁,y₁) (x₂,y₂) (x₃,y₃): A(-10,30), B(30,50, C(-40,20)
XY = 1/2 AC , YZ = 1/2 AB , ZX = 1/2 BC
X (10,40) , Y (-5,35) , Z (-25,25) : X(x'₁,y'₁), Y(x'₂,y'₂), Z(x'₃,y'₃)
area of triangle by 3 vertices: (x₁,y₁) (x₂,y₂) (x₃,y₃) is
a = abs[x₁(y₂-y₃)+x₂(y₃-y₁)+x₃(y₁-y₂)] / 2 ... this is just a common formula for any triangle
a = abs(-10*30 + 30*-10 + -40*-20) / 2 = 100
a' = abs(10*10 + -5*-15 + -25*5) / 2 = 25
a/a' = 100/25 = 4/1
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Answer:
The car requires 192 feet to stop from a speed of 48 miles per hour on the same road
Step-by-step explanation:
- Direct proportion means that two quantities increase or decrease in the same ratio
- If y is directly proportional to x (y ∝ x) , then
<em>OR</em> y = k x, where k is the constant of proportionality
∵ The stopping distance d of an automobile is directly
proportional to the square of its speed s
- That means d ∝ s²
∴
∵ A car requires 75 feet to stop from a speed of 30 miles per hour
∴ d = 75 feet
∴ s = 30 miles/hour
- Change the mile to feet
∵ 1 mile = 5280 feet
∴ 30 miles/hour = 30 × 5280 = 158400 feet/hour
∵ The car require to stop from a speed of 48 miles per hour
on the same road
- Change the mile to feet
∴ 48 miles/hour = 48 × 5280 = 253440 feet/hour
∵
- Substitute the values of by 75 feet,
by 158400 feet/hour
and by 253440 feet/hour
∴
∴
- By using cross multiplication
∴ 25 × = 75 × 64
- Divide both sides by 25
∴ = 192 feet
The car requires 192 feet to stop from a speed of 48 miles per hour on the same road